Non-stationary support iterations of Prikry Forcings and Restrictions of Ultrapower Embeddings to the Ground Model

Moti Gitik; Eyal Kaplan

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arXiv · 2109.10618

Non-stationary support iterations of Prikry Forcings and Restrictions of Ultrapower Embeddings to the Ground Model

Moti Gitik·Eyal Kaplan

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Abstract

We study the nonstationary-support iteration of Prikry forcings below a measurable cardinal \kappa, characterizing all the normal measures it carries in the generic extension. We then analyze the restriction of ultrapower embeddings, taken with such a normal measure in the generic extension, to the ground model. We prove that every such restriction is an iterated ultrapwer of the ground model, and provide a sufficient condition for its definability there. This is done without core-model theoretic arguments: the assumption that GCH holds in the ground model up to \kappa suffices.

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BibTeX RIS

Moti Gitik, Eyal Kaplan. 2021-09-22. Non-stationary support iterations of Prikry Forcings and Restrictions of Ultrapower Embeddings to the Ground Model. https://arxiv.org/abs/2109.10618

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